In the standings, Piquet leads di Grassi by 17 points ahead of the double-header race weekend of Battersea Park's London ePrix.
In an interview the only thing that they could agree upon was that they would "never be friends".
"I was [Sebastien] Buemi's teammate [in GP2 in 2007], and we had our fights on the track, but outside it was fine," said di Grassi. "Actually, all drivers are polite. Not Nelsinho, he is rude and speaks a lot of nonsense.
"He tends to do more or less what his father did, in a completely different level, but having the same style, causing controversy, and that's why it is difficult to have a friendship outside the track," he added.
Piquet had nothing positive to say about di Grassi only that he "talked too much".
"I was never friends with Lucas," he said. "We are very different people and I think this is one of the reasons why we are not friends outside the track.
"I am friendly with some drivers and we even have vacations together, people like Bruno Senna, but some personalities do not match. It seems to be our case.
"Maybe it was because of when he was part of the Renault junior program and they ended up choosing me to race in F1. Maybe he wasn't too happy about that,” said Piquet.
"The main thing was Monaco [where he claimed di Grassi blocked him in qualifying], that upset me. The press has used that to relive the whole rivalry story.
"I talk too much? He was the one who talked too much. Especially after Berlin [where di Grassi lost a victory due to a technical ruling].
"I am doing my thing, my job. Who knows after the end of the championship I may say what I need to say," he added.